MOSCOW — There may be little that pleases Senator Rand Paul, the libertarian-leaning Kentucky Republican, more than thumbing his nose at Washington groupthink.

So it was on Monday when Mr. Paul, decamping for the Senate’s one-week recess, took his lonely defense of President Trump’s Russia policy to Moscow to deliver a show of contrarianism all too familiar to his colleagues back home.

“I’ve traveled here to say that there are many Americans who want to have diplomacy, that want to have engagement; I’m one of them,” Mr. Paul said, standing beside Konstantin Kosachyov, the chairman of the foreign relations committee of Russia’s senate who has been subject to American sanctions since April.

At home, Mr. Paul’s fellow senators speak in grave tones about how to respond to an alarming pace of revelations about the scope and durability of Russia’s campaign to undermine the democratic process — an effort that American intelligence officials warn remains active despite American retaliation. One plan, introduced last week by three Republicans and three Democrats, calls for “crushing” new sanctions.

Mr. Paul has something else in mind — maybe even taking some Russian lawmakers back to Washington.

“Our biggest issue right now is no dialogue,” Mr. Paul said. “It isn’t the issues at hand. The issue is that we can’t have discussion of issues because we have no dialogue.”

As he stepped out of a meeting with senators of the Federation Council, the upper chamber of Russia’s parliament, on Monday, Mr. Paul said that he had extended an invitation to members of its foreign policy committee to visit Washington. The two sides would also try to arrange a meeting in a neutral third country, he said — which presumably would allow Mr. Kosachyov to attend without the pesky issue of sanctions hanging over his head.

Later in the day, in a meeting with members of Russia’s lower house of parliament, Mr. Paul said he would oppose the passage of new Russia sanctions proposed by his Senate colleagues. He complained about “sanctions hysteria” in Washington, according to a report by RIA Novosti, a Russian state-run news agency.

For good measure, he chatted up Sergey I. Kislyak, the former Russian ambassador to the United States whose meetings with Michael T. Flynn, who would become Mr. Trump’s first national security adviser; Jeff Sessions, who would become attorney general; and Jared Kushner, the president’s son-in-law, are at the heart of the Russia investigation.

For their part, Russian lawmakers pressed Mr. Paul to intervene on behalf of Maria Butina, the 29-year-old gun rights activist being held as a Russian agent.

“If you, Senator Paul, stand up in defense of Maria Butina, even in order to get her restrictive measure changed, even to get her released from custody — and we are seeking her release and the opportunity for her to return to her homeland — you will really show yourself to be a real human being,” the Interfax news agency quoted the lawmaker Leonid Slutsky saying.

Mr. Paul was the only lawmaker on the trip, which was financed by the Cato Institute, a leading libertarian research organization in Washington. He was accompanied by Peter Goettler, Cato’s president and chief executive, and Don Huffines, a Texas state senator who was chairman of Mr. Paul’s presidential campaign in the state.

Speaking to journalists, Mr. Kosachyov denied that Russia interfered in the 2016 presidential election and said that it would not intervene in future races.

“We had a constructive meeting and agreed on concrete plans on how we can restore contacts between our committees in the near future,” Mr. Kosachyov said. “We are absolutely ready for this. The rest is up to the American side.”

Mr. Paul described his meeting with senators of the Federation Council as “very successful,” saying that he came to Moscow “to renew diplomacy, engagement and communications with Russia.”

Mr. Paul, a former ophthalmologist who ran for president in 2016, is one of the Senate’s loudest critics of interventionist foreign policy. But his stance on Russia has not always been so warm. In 2014, after Russia annexed Crimea, he wrote that the United States must isolate Moscow “if it insists on acting like a rogue nation.”

Russia’s relations with the West have not improved since then, as Moscow has backed rebels in eastern Ukraine, played a central part in supporting the government in Syria’s civil war, interfered in other countries’ elections, and been accused of using a nerve agent in an assassination attempt on British soil.

And while other lawmakers may be incensed by Russia’s meddling in American elections, Mr. Paul has suggested that the United States has done the same thing.

“Russia shouldn’t meddle in our elections,” he wrote on Twitter last month. He added: “U.S. shouldn’t do it either. We also should remain rational and not risk war by yelling war crime.”

The trip was the second high-profile visit by an American delegation to Russia within several weeks. Eight Republican lawmakers visited Moscow ahead of the summit meeting in Helsinki, Finland, between Mr. Trump and President Vladimir V. Putin of Russia in July. The Russian news media depicted the senators’ overtures as evidence that relations between the two countries were moving in Russia’s favor.

Mr. Trump’s performance at the meeting was viewed even less kindly. But that has not stopped the president from pushing ahead with his campaign to warm relations: Just days after he returned, Mr. Trump said he planned to invite Mr. Putin to Washington.

Ivan Nechepurenko reported from Moscow, and Nicholas Fandos from Washington.

A version of this article appears in print on , on Page A7 of the New York edition with the headline: A Senator’s Lonely Outreach in Moscow. Order Reprints | Today’s Paper | Subscribe